1. Detection of Dairy Herds at risk for changing Salmonella Dublin status Symposium in Applied Statistics 2012 Anders Stockmarr DTU Data Analysis Technical University of Denmark anst@imm.dtu.dk Rene Bødker, DTU National Vet. Inst. Liza Nielsen, Dept. of Large Animal Sciences, Univ. of Copenhagen

2. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” Background Salmonella Dublin (S. Dublin) is a specific serotype of the Salmonella bacterium S. Dublin is host-adapted to cattle, and the most prevalent serotype found in cattle in Denmark (~60-70% of all isolates) S. Dublin is a rare but serious zoonosis that causes severe disease and deaths in humans every year (10-40 hospitalized cases per year in Denmark). Detecting Dairy Herds25/01/20122

3. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” S. Dublin Symptoms Unthrifty calves Fever Diarrhoea (bloody) Pneumonia Death Abortions 3Detecting Dairy Herds25/01/2012

4. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” The Salmonella Dublin surveillance and eradication programme in Denmark Eradication campaign until 2014 Goal: The Danish cattle population free from Salmonella Dublin in 2014 2010-2012: Sanctions to improve motivation 2013-2014: Veterinary Authorities will handle infected herds through law enforcement Detecting Dairy Herds25/01/20124

5. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” The Salmonella Dublin surveillance and eradication programme in Denmark Surveillance program since 2002: Cattle herds are classified as follows, based on Bulk Tank Milk/blood sample antibodies and trade contacts: Level 1: Most likely free from salmonella Level 2: Too high antibody levels or contact to other herds in Level 2 or 3 Level 3: Clinical Salmonella Dublin diagnosis and culture positive Unknown: Only non-dairy herds with too few samples to classify (hobby herds) Detecting Dairy Herds25/01/20125

6. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” The Salmonella Dublin surveillance and eradication programme in Denmark Surveillance program since 2002: Cattle herds are classified as follows, based on Bulk Tank Milk/Blood sample antibodies and trade contacts: Level 1: Most likely free from salmonella Level 2: Too high antibody levels or contact to other herds in Level 2 For the present work we do not distinguish between level 2 and 3 Detecting Dairy Herds25/01/20126

7. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” Reasons for assigning Level 1 to dairy herds Salmonella Dublin Level 1 is given if: 1. Valid bulk tank milk antibody measurements exists – and 2. The last 4 bulk tank milk antibody measurements, gathered with at least 3 weeks in between, shows an average ODC-value of less than 25 – and 3. The latest Salmonella Dublin measurement has not shown an increase of more than 20, compared to the average of the three preceding measurements - and 4. A number of circumstances mainly related to trade and missing data do not hold. Otherwise, Salmonella Dublin Level 2 is given. Detecting Dairy Herds25/01/20127

8. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” Bulk Tank Milk antibody measurements from dairy herds Collected routinely every three months. Thus, a very long period for an infection to develop before a dairy herd is possibly re-classified. Sanctions and law enforcement gives farmers an incentive to act if they suspect an infection is present. There is therefore a need to identify herds at risk of changing S. Dublin level, based on information a quarter earlier than re- classification takes place. Detecting Dairy Herds25/01/20128

9. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” Risk Herds Are herds ’at risk of’ changing level from 1 to 2; we will start out with this loose definition. Risk herds are thus Level 1 (”Status 1”) herds. Purpose of current study: To determine appropriate definitions for a risk herd, based on available factors one quarter prior to a possible level shift. Detecting Dairy Herds25/01/20129

10. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” The probability of changing S. Dublin status 10Detecting Dairy Herds25/01/2012 If X i,t denotes the BTM measurement for herd i at time t, and the mean of the last 3 measurements, then the probability of a status change is given as ie. is modeled through a logistic regression: through successive conditioning on the BTM measurements.

11. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” What makes herds become Risk Herds? - bulk tank milk measurements, trade, neighbors and herd size Bulk tank milk measurements: –High antibody levels; –Unstable development in measurements. Trade: –That animals are bought from herds that turn out to be Status 2 herds; –that many animals are bought; –that many herds are traded with. Neighbors: –That many neighbors are assigned Status 2; –That there are many neighbors. Size: –That the herd is large. 11Detecting Dairy Herds25/01/2012

12. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” Available Data Quarterly bulk tank milk measurements 2002-2008 for 9397 dairy herds; Geographical coordinates for dairy and non-dairy cattle herds and their quarterly S. Dublin level; All perfomed trades at animal level 2002-2008; Data on herd sizes; Only 2004-2008 er usable. 12Detecting Dairy Herds25/01/2012

13. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” BTM measurements and Alarm Herds BTM measurement enter covariates through ; obviously a high level of recent antibody levels will increase the risk of a Status 2 change. But also sudden (upwards) deviations from a stationary development could indicate an emerging infection. BTM measurements also enters through Alarm Herd status: Alarm Herd concept: A Status 1 herd A is an Alarm Herd at a timepoint t 0, if BTM measurements for A for at least the previous 4 time points do not vary more than a standard 95% confidence interval would predict, and the BTM measurement for A at time t 0 is above this level, and above an upward threshold c > 0. 13Detecting Dairy Herds25/01/2012

14. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” Alarm Herds Alarm Herds are Level 1 herds: The jump from the steady progression should be big (to a level > c),but not so big that it triggers a Status 2 classification. Time points where BTM measurements for A for at least the previous 4 time points do not vary more than a standard 95% confidence interval would predict are called stable timepoints. When a herd leaves a stable state to become unstable, we say that a jump has occurred. When a herd becomes an Alarm Herd, we say that a risk jump has occurred. 14Detecting Dairy Herds25/01/2012

15. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” A BTM measurement progression example 15Detecting Dairy Herds25/01/2012

16. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” Estimation of c We included Alarm Herd status in the basic logistic regression model with varying values of c (integer ODC values), to gain a series of competing models; We chose the model with the optimal Akaike Information; Consequently, we estimated c to be 13. 16Detecting Dairy Herds25/01/2012

17. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” Trade information 17Detecting Dairy Herds25/01/2012

18. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” Trade 18Detecting Dairy Herds25/01/2012

19. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” Trade II 19Detecting Dairy Herds25/01/2012

20. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” Trade III 20Detecting Dairy Herds25/01/2012

21. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” Trade IV 21Detecting Dairy Herds25/01/2012

22. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” Neighbor herds and animals 22Detecting Dairy Herds25/01/2012

23. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” Neighbors – What is a neighbor? Ersbøll & Nielsen (2008): 4.9 km is the average ’range of influence’ for local spread of Salmonella. We define Neighbors to be herds with a distance of less than 4.9 km from the herd in question. Counted for all dairy herds in Denmark, dynamically (ie., a time series). We consider both the number of herds and the number of animals within this radius. The neighbor effect is a hidden geographical component, in that clusters of herds will have many Neighbors (well known places in Jutland). 23Detecting Dairy Herds25/01/2012

24. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” Herd Sizes, dairy herds 24Detecting Dairy Herds25/01/2012

25. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” Herd sizes, non-dairy herds (used as neighbors only) 25Detecting Dairy Herds25/01/2012

26. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” Dynamic herd sizes, dairy herds 26Detecting Dairy Herds25/01/2012

27. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” Dynamic herd sizes, non-dairy herds 27Detecting Dairy Herds25/01/2012

28. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” Explanatory variableType of effect Mean of explanatory variable Regression coefficient ± S.E. P InterceptMain effect14.90 ± 0.20<0.0001 Season, 1st quarterSeasonal effect0.27-6.80 ± 0.30<0.0001 Season, 2 nd quarterSeasonal effect0.26-7.14 ± 0.32<0.0001 Season, 3 rd quarterSeasonal effect0.26-6.62 ± 0.29<0.0001 Mean of last 3 (Mean3)Main effect5.34 0.12 ±0.016<0.0001 Mean3, 1 st quarter**Interaction5.25*0.071± 0.021<0.0001 Mean3, 2 nd quarterInteraction5.27*0.11 ± 0.022<0.0001 Mean 3, 3 rd quarterInteraction5.47*0.067 ± 0.021<0.0001 Trade contacts with Status 2 herds Main effect0.037 0.44 ± 0.21- Animals traded with Status 1 herds Main effect2.625.30e-3 ± 3.44e-3- Animals traded with Status 2 herds Main effect0.290.033 ± 0.010- Neighbour Status 2 dairy herdsMain effect4.28 0.066± 0.033- Neighbour animals from Status 2 dairy herds Main effect8164.01e-4 ± 1.61e-4- Alarm1Main effect0.019 0.58± 0.320.001 Mean3× Animals traded with Status 2 herds Interaction2.51-1.14e-3 ± 6.41e-4<0.0001 Mean 3 × Neighbour animals from Status 2 dairy herds Interaction5370-1.27e-5 ± 5.70e-6<0.0001 Trade contacts with Status 2 herds × Animals traded with Status 2 herds Interaction0.40-9.33 e-3± 6.21e-3<0.0001 Neighbour Status 2 dairy herds × Neighbour animals from Status 2 dairy herds Interaction8250-1.69e-5 ± 0.73e-6<0.0001 28Detecting Dairy Herds25/01/201 2

29. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” Remarks I No effect of trade two quarters back. Interaction across groups of covariates with only. Alarm Herd status (one quarter back) has a large impact; Effect of animals (traded and neighbors) decreases when level of increases; those with a high level of have a risk independent of animals purchased and animals traded. Independent of : Trade contacts with Status 2 herds and Alarm Herd status. 29Detecting Dairy Herds25/01/2012

30. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” Remarks II Trade with Status 1 herds has an effect through the number of purchased animals, while trade with Status 2 herds has an effect both through the number of trade partners and the number of purchased animals. Status 1 trade contacts is not significant. Neighbors has an effect through Status 2 dairy neighbor farms and Status 2 dairy animals. Non-dairy neighbours and Status 1 dairy neighbors are not significant. 30Detecting Dairy Herds25/01/2012

31. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” Model based on 2007 data only Table 2 Explanatory variables, regression coefficients and P-values in the final logistic regression model for a change in herd classification from Status 1 to Status 2 in the Danish surveillance programme for S. Dublin in dairy herds, base on data from 2007 Explanatory variable Type of effect Mean of explanatory variable Regression coefficient ± S.E. p InterceptMain effect1-7.05 ± 0.39<0.0001 Mean3Main effect6.500.22 ± 0.02<0.0001 Trade contacts with Status 2 herds Main effect0.0480.70 ± 0.370.0006 Number of animals in neighbouring Status 2 dairy herds Main effect7580.0179 ± 0.01130.003 Alarm1Main effect0.0231.08 ±0.690.006 31Detecting Dairy Herds25/01/2012

32. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” Risk Scores We used the linear predictor as a risk score index. Which index value is high enough to consider a given herd to be a ’risk herd’, where the farmer should intervene if possible? 32Detecting Dairy Herds25/01/2012

33. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” Risk Scores – big model 33Detecting Dairy Herds25/01/2012

34. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” Risk Scores – small model 34Detecting Dairy Herds25/01/2012

35. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” Definitions of risk herds A threshold r that defines a herd to be a risk herd if the risk score is > r represents a trade-off between number of herds at risk and the frequency with which they change status: 35Detecting Dairy Herds25/01/2012

36. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” Predictive power 36Detecting Dairy Herds25/01/2012 Big model Small model Coefficients re-estimated based on 2004-2006 data, and used to predict 2007 data: ROC curves when threshold varies

37. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” Small model versus big model Tempting to choose the simpler model; Predictive power is similar and model is much less complicated; However, the model could not be reproduced in full when applied to different cohorts of the data; we have no explanation for this. We recommend use of the big model. 37Detecting Dairy Herds25/01/2012

38. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” Predictive power and relative importance Threshold is optimized based on predictive power of the big model as r = -1.05 However, it is much more important to predict those that change status than those that do not. Let α denote the importance of predicting a status change correctly relative to a non-change, and let C be the event “change of status”, and PC the event that a herd is classified as a Risk Herd. Instead of optimizing average predictability, we optimise the importance function αP(C|PC)P(PC)+P(C ¬ |PC ¬ )P(PC ¬ ) where “ ¬ ” signifies negation. 38Detecting Dairy Herds25/01/2012

39. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” Threshold value as a function of importance 39Detecting Dairy Herds25/01/2012

40. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” Suggested estimation of α based on farmer incentive Loss if a Status 2 herd is not correctly predicted: Price[3 months in Status 2] -Price[3 months in Status 2]* P(Interventions fail) -Price[Interventions] Loss if a Status 1 herd is not correctly predicted: Price[Interventions] 40Detecting Dairy Herds25/01/2012

41. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” Suggested estimation of α based on societal costs Replace Price[3 months in Status 2] by R 0 [ Price[3 months in Status 2] +cost(human infections) per herd] where R 0 denotes the average excess number of infected herds due to delayed identification. Higher α and lower threshold r. These cost values are not known and dependent on legislation 41Detecting Dairy Herds25/01/2012

42. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” Geographical distribution of risk herds ( α =5) 3 rd quarter 2007. 42Detecting Dairy Herds25/01/2012

43. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” Conclusion We suggest that risk herds may be defined as herds with a risk score over a threshold r, with r taking a value from -1.05 and lower, depending on the nature of sanctions and the importance of detecting status changes. Potential uses if risk index: replacement of the current classification system; potential legal conflicts should be clarified. Alternatively, a mandatory notice to the farmer on a risk herd classification, allowing voluntary interventions; Coming legislation should encourage farmers to intervene. However, cost to society is higher than the cost to individual farmers due to spread of disease, so a higher α value and thus lower threshold r could apply. 43Detecting Dairy Herds25/01/2012

44. DTU Informatics, Technical University of Denmark Add Presentation Title in Footer via ”Insert”; ”Header & Footer” Acknowledgement We thank Jørgen Nielsen from the Danish Cattle Federation for providing register data from the Danish Cattle Database. Thanks Jørgen. 44Detecting Dairy Herds25/01/2012